Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
typedef long double ld;

int main() {
    int N;
    cin >> N;
    ld a[N], ans = 0;
    for (auto &x : a) cin >> x;
    vector<pair<ld, int>> tmp;
    for (int i = 0; i < N; i++) {
        tmp.push_back(make_pair(a[i], i));
    }
    sort(tmp.begin(), tmp.end());
    vector<int> index;
    for (int i = N - 4; i < N; i++) {
        index.push_back(tmp[i].second);
    }
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (i == j) continue;
            ld C = a[i];
            ld D = a[j];
            vector<int> MAX;
            for (int k = 3; 0 <= k && MAX.size() != 2; k--) {
                if (index[k] != i && index[k] != j) {
                    MAX.push_back(index[k]);
                }
            }
            ans = max(ans, (a[MAX[0]] + a[MAX[1]]) / (C - D));
        }
    }
    cout << fixed << setprecision(10) << ans << endl;
}